How to Derive a Formula

Will artificial intelligence solve all problems, making scientific formulae redundant? The authors of this book would argue that there is still a vital role in formulating them to make sense of the laws of nature. To derive a formula one needs to follow a series of steps; last of all, check that the result is correct, primarily through the analysis of limiting cases. The book is about unravelling this machinery.

Mathematics is the 'queen of all sciences', but students encounter many obstacles in learning the subject — familiarization with the proofs of hundreds of theorems, mysterious symbols, and technical routines for which the usefulness is not obvious upfront. Those interested in the physical sciences could lose motivation, not seeing the wood for the trees.

How to Derive a Formula is an attempt to engage these learners, presenting mathematical methods in simple terms, with more of an emphasis on skills as opposed to technical knowledge. Based on intuition and common sense rather than mathematical rigor, it teaches students from scratch using pertinent examples, many taken across the physical sciences.

This book provides an interesting new perspective of what a mathematics textbook could be, including historical facts and humour to complement the material.
Contents: PrefaceIntroductionFrom Base Camp — Understanding Functions and Variables: The First Stage:Essential FunctionsPolynomial Expansions: When They Work and When They Don'tLimits, Differentiation and IntegrationThe Way to Check Yourself: Analysis of Limiting CasesDefinite Integrals as Functions Probability Distribution Functions, and Filter Functions as Limiting CasesVectors and Introduction to Vector CalculusUnderstanding Sequences and SeriesComplex NumbersDimensionality and ScalingConcluding RemarksProblemsFrom Camp 1: Deeper Understanding of Functions and Solving Equations:Introduction to Functions of Two or More VariablesFourier Series and IntegralsLinear Equations and DeterminantsMatrices and SymmetrySolving Nonlinear Equations, Algebraic and TranscendentalIntroduction to Ordinary Differential EquationsFurther Methods for Evaluating the Integrals and the Gamma FunctionFunctions of a Complex VariableConcluding RemarksProblemsInstructions to Access the Outlines of Solutions
Readership: Advanced and enthusiastic school students preparing for universities, specializing in science — A-level (UK), Abitur (Germany), Lycée (France), high school (USA) and alike; teachers and tutors; undergraduate students; university lecturers.Mathematics for Physical Scientists;Practical Math;Theoretical Skills;Approximation Methods;Asymptotic Analysis;Solving Equations;Testing and Understanding Results0Key Features:This book emphasizes on skills, tricks, approximations, testing and understanding results, learning through not only mathematical, but the vast number of physical examplesEngaging and exciting, the book is complemented with amusing statements and cartoons, historical anecdotes, and use of colour in insightful diagrams and plotsThe book teaches in 'interactive' mode: some of the longer examples are cumulative case studies, demonstrating a set of methods in one go, which contain intermediate calculations as exercises